Quotient group

Let G be a group and let N be a normal subgroup of G. Then [math]\displaystyle{ G/N=\{gN:g\in{G}\} }[/math] is the set of all cosets of N in G and is called the quotient group of N in G.

This group is used in the proof of Lagrange's Theorem, for instance. In fact, the proof of Lagrange's theorem establishes that if

G is finite, then [math]\displaystyle{ |G/H|=|G|/|H| }[/math].

Quotient Group Media

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  The cosets of the fourth roots of unity N in the twelfth roots of unity G.